| $\sim (A \ \&\ B) \rightarrow H$ |
| $F\ v \sim (H \ \&\ F)$ |
| $(A \ \&\ B) \rightarrow (H \ \&\ F)$ |
| $\sim F \ \&\ (D \ \&\ E)$ |
| $(D \ \&\ E) \ \&\ H$ |
| $(1)\ \sim (A \ \&\ B)\ \rightarrow H$ | $P$ |
| $(2)\ F\ v \sim (H \ \&\ F)$ | $P$ |
| $(3)\ (A \ \&\ B)\ \rightarrow (H \ \&\ F)$ | $P$ |
| $(4)\ \sim F \ \&\ (D \ \&\ E)$ | $P/ (D \ \&\ E)\ \&\ H$ |
| $(5)\ \sim F$ | $4,$ Simp. |
| $(6)\ \sim (H \ \&\ F)$ | $2, 5, DS$ |
| $(7)\ \sim (A \ \&\ B)$ | $3, 6, MT$ |
| $(8)\ H$ | $1, 7, MP$ |
| $(9)\ D \ \&\ E$ | $4,$ Simp. |
| $(10)\ (D \ \&\ E)\ \&\ H$ | $9, 8,$ Conj. |
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
| $G \rightarrow H$ |
| $(A\ v\ B) \rightarrow D$ |
| $D \rightarrow [(S\ \&\ T) \rightarrow P]$ |
| $(S\ \&\ T)\ v\ G$ |
| $A\ v\ B$ |
| $(P\ v\ H)\ \&\ D$ |
| $(Q\ \&\ B)\ v\ \sim D$ |
| $(Q\ \&\ B) \rightarrow \sim E$ |
| $F \rightarrow \sim\ \sim E$ |
| $\sim D \rightarrow (L\ \&\ N)$ |
| $F$ |
| $L\ v\ (B\ \&\ D)$ |
| $A \rightarrow J$ |
| $B \rightarrow R$ |
| $(A\ v\ B)\&\ \sim D$ |
| $J \rightarrow D$ |
| $\therefore (D\ v\ R)\ \&\ (B\ v\ K)$ |
| $(H\ \&\ K)\ \rightarrow\ (J\ v\ K)$ |
| $\sim\ E\ \&\ \sim\ F$ |
| $F\ v\ \sim\ (J\ v\ K)$ |
| $\sim\ (H\ \&\ K)\ \rightarrow\ H$ |
| $H\ \&\ \sim\ E$ |
| $(P\ \&\ Q) \rightarrow R$ |
| $R \rightarrow (H \rightarrow G)$ |
| $H\ \&\ K$ |
| $P\ \&\ Q$ |
| $\therefore (G\ v\ I)\ \&\ H$ |
| $T \rightarrow B$ |
| $B \rightarrow ( \sim\ P \rightarrow\ \sim\ Q)$ |
| $\sim\ P\ \&\ \sim\ R$ |
| $T$ |
| $\therefore\sim\ Q\ v\ X$ |